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Model-averaged estimates/intervals/distributions #771
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library(MATA) library(parameters) set.seed(0) n = 20 # 'n' is assumed to be even x1 = c(rep(0,n/2), rep(1,n/2)) # two groups: x1=0, and x1=1 x2 = rnorm(n, mean=10, sd=3) y = rnorm(n, mean = 3*x1 + 0.1*x2) # data generation x1 = factor(x1) m1 = glm(y ~ x1) # using 'glm' provides AIC values. m2 = glm(y ~ x1 + x2) # using 'lm' doesn't. aic = c(m1$aic, m2$aic) delta.aic = aic - min(aic) model.weights = exp(-0.5*delta.aic) / sum(exp(-0.5*delta.aic)) residual.dfs = c(m1$df.residual, m2$df.residual) p1 = predict(m1, se = TRUE, newdata = list(x1 = factor(0), x2 = 10.64), type = "link") p2 = predict(m2, se = TRUE, newdata = list(x1 = factor(0), x2 = 10.64), type = "link") theta.hats = c(p1$fit, p2$fit) se.theta.hats = c(p1$se.fit, p2$se.fit) # 95% MATA-Wald confidence interval for theta: mata.wald(theta.hats, se.theta.hats, model.weights, mata.t = TRUE, residual.dfs = residual.dfs) #> [1] 0.6196654 1.6516695 parameters:::averaged_parameters(m1, m2) #> [1] 0.619622 1.651641
Created on 2022年09月05日 with reprex v2.0.2
@bwiernik implementation seems to work, but I'm not sure about the meaning of this function. It returns one estimate (in the above example currently only CIs)? What does this estimate represent?
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Sep 5, 2022
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@@ Coverage Diff @@ ## main #771 +/- ## ========================================== - Coverage 52.99% 52.85% -0.14% ========================================== Files 184 185 +1 Lines 12706 12738 +32 ========================================== Hits 6733 6733 - Misses 5973 6005 +32
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No, that's not right. It should be output with the same structure as the input vectors, averaged across models (eg, if 32 predictions from 2 models, then output should be 32 predictions, weighted across the two models). The MATA CIs for the 32 predictions would then be the values for each prediction that satisfy the critical value when averaged across models
cf #768